1. Industrial Control
Behzad Samadi
Department of Electrical Engineering
Amirkabir University of Technology
Winter 2009
Tehran, Iran
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2. Thermal Systems
Electrical Analogy
Type of System Electrical Thermal
T-Variable i, current q, heat flow
A-Variable v, voltage T, temperature
Resistance resistor thermal resistor
Storage (A-Type) capacitor thermal capacitor
Storage (T-Type) inductor unknown
Note that q is in units of power and no T-type thermal energy storage
has been identified.
[Ogata, 1997]
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3. Heat Transfer
Conduction: Heat transfer through solid media
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4. Heat Transfer
Conduction: Heat transfer through solid media
T1 − T2 =Rcq
Rc =
d
KA
d =thickness of the wall
A =area of the wall
K =thermal conductivity of the wall’s material
[Macia and Thaler, 2004]
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5. Heat Transfer
Convection: Heat transfer through a fluid (liquid or gas)
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6. Heat Transfer
Convection: Heat transfer through a fluid (liquid or gas)
T1 − T2 =Rhq
Rc =
d
hA
d =thickness
A =area
h =convection coefficient
[Macia and Thaler, 2004]
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7. Heat Transfer
Radiation:
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8. Heat Transfer
Radiation:
q =AεFσ(T4
1 − T4
2 )
A =area of the surface of the object of interest
ε =parameter descriptive of the emission of surfaces 1 and 2
σ =Stefan-Boltzman Constant
F =geometrical shape factor
T1, T2 =absolute temperatures of bodies 1 and 2
[Macia and Thaler, 2004]
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9. Heat Transfer
Radiation:
q =AεFσ(T4
1 − T4
2 )
Rr =
1
AεFσ(T2
1 + T2
2 )(T1 + T2)
⇒ T1 − T2 = Rr q
[Macia and Thaler, 2004]
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10. Thermal Capacitance
q =C
dT
dt
C =mcx
C =thermal capacitance of the object
m =mass of the object
cx =specific heat of material
[Macia and Thaler, 2004]
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11. Macia, N. F. and Thaler, G. J. (2004).
Modeling and Control of Dynamic Systems.
Delmar Learning.
Ogata, K. (1997).
Modern Control Engineering.
Prentice Hall, 3 edition.
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